Parametric policy search algorithms are one of the methods of choice for the optimisation of Markov Decision Processes, with Expectation Maximisation and natural gradient ascent being considered the current state of the art in the field. In this article we provide a unifying perspective of these two algorithms by showing that their step-directions in the parameter space are closely related to the search direction of an approximate Newton method. This analysis leads naturally to the consideration of this approximate Newton method as an alternative gradient-based method for Markov Decision Processes. We are able show that the algorithm has numerous desirable properties, absent in the naive application of Newton's method, that make it a viable alternative to either Expectation Maximisation or natural gradient ascent. Empirical results suggest that the algorithm has excellent convergence and robustness properties, performing strongly in comparison to both Expectation Maximisation and natural gradient ascent.

In this work we use Branch-and-Bound (BB) to efficiently detect objects with deformable part models. Instead of evaluating the classifier score exhaustively over image locations and scales, we use BB to focus on promising image locations. The core problem is to compute bounds that accommodate part deformations; for this we adapt the Dual Trees data structure to our problem. We evaluate our approach using Mixture-of-Deformable Part Models. We obtain exactly the same results but are 10-20 times faster on average.

An important way to make large training sets is to gather noisy labels from crowds of nonexperts. We propose a minimax entropy principle to improve the quality of these labels. Our method assumes that labels are generated by a probability distribution over workers, items, and labels. We infer the ground truth by minimizing the entropy of this distribution, which we show minimizes the Kullback-Leibler (KL) divergence between the probability distribution and the unknown truth. We show that a simple coordinate descent scheme can optimize minimax entropy.

We study the problem of diverse feature selection in linear regression: selecting a small subset of diverse features that can predict a given objective. Diversity is useful for several reasons such as interpretability, robustness to noise, etc. We propose several spectral regularizers that capture a notion of diversity of features and show that these are all submodular set functions. These regularizers, when added to the objective function for linear regression, result in approximately submodular functions, which can then be maximized approximately by efficient greedy and local search algorithms, with provable guarantees. We compare our algorithms to traditional greedy and $\ell_1$-regularization schemes and show that we obtain a more diverse set of features that result in the regression problem being stable under perturbations.

Bayesian model-based reinforcement learning is a formally elegant approach to learning optimal behaviour under model uncertainty, trading off exploration and exploitation in an ideal way. Unfortunately, finding the resulting Bayes-optimal policies is notoriously taxing, since the search space becomes enormous. In this paper we introduce a tractable, sample-based method for approximate Bayes-optimal planning which exploits Monte-Carlo tree search. Our approach outperformed prior Bayesian model-based RL algorithms by a significant margin on several well-known benchmark problems -- because it avoids expensive applications of Bayes rule within the search tree by lazily sampling models from the current beliefs. We illustrate the advantages of our approach by showing it working in an infinite state space domain which is qualitatively out of reach of almost all previous work in Bayesian exploration.

We consider the problem of identifying a sparse set of relevant columns and rows in a large data matrix with highly corrupted entries. This problem of identifying groups from a collection of bipartite variables such as proteins and drugs, biological species and gene sequences, malware and signatures, etc is commonly referred to as biclustering or co-clustering. Despite its great practical relevance, and although several ad-hoc methods are available for biclustering, theoretical analysis of the problem is largely non-existent. The problem we consider is also closely related to structured multiple hypothesis testing, an area of statistics that has recently witnessed a flurry of activity. We make the following contributions: i) We prove lower bounds on the minimum signal strength needed for successful recovery of a bicluster as a function of the noise variance, size of the matrix and bicluster of interest.

Generalized Linear Models (GLMs) and Single Index Models (SIMs) provide powerful generalizations of linear regression, where the target variable is assumed to be a (possibly unknown) 1-dimensional function of a linear predictor. In general, these problems entail non-convex estimation procedures, and, in practice, iterative local search heuristics are often used. Kalai and Sastry (2009) provided the first provably efficient method, the \emph{Isotron} algorithm, for learning SIMs and GLMs, under the assumption that the data is in fact generated under a GLM and under certain monotonicity and Lipschitz (bounded slope) constraints. However, to obtain provable performance, the method requires a fresh sample every iteration. In this paper, we provide algorithms for learning GLMs and SIMs, which are both computationally and statistically efficient. We modify the isotonic regression step in Isotron to fit a Lipschitz monotonic function, and also provide an efficient $O(n \log(n))$ algorithm for this step, improving upon the previous $O(n 2)$ algorithm.

A hallmark of modern machine learning is its ability to deal with high dimensional problems by exploiting structural assumptions that limit the degrees of freedom in the underlying model. A deep understanding of the capabilities and limits of high dimensional learning methods under specific assumptions such as sparsity, group sparsity, and low rank has been attained. Efforts (Negahban et al., 2010, Chandrasekaran et al., 2010} are now underway to distill this valuable experience by proposing general unified frameworks that can achieve the twin goals of summarizing previous analyses and enabling their application to notions of structure hitherto unexplored. Inspired by these developments, we propose and analyze a general computational scheme based on a greedy strategy to solve convex optimization problems that arise when dealing with structurally constrained high-dimensional problems. Our framework not only unifies existing greedy algorithms by recovering them as special cases but also yields novel ones.

We consider a generalization of mixed regression where the response is an additive combination of several mixture components. Standard mixed regression is a special case where each response is generated from exactly one component. Typical approaches to the mixture regression problem employ local search methods such as Expectation Maximization (EM) that are prone to spurious local optima. On the other hand, a number of recent theoretically-motivated \emph{Tensor-based methods} either have high sample complexity, or require the knowledge of the input distribution, which is not available in most of practical situations. In this work, we study a novel convex estimator \emph{MixLasso} for the estimation of generalized mixed regression, based on an atomic norm specifically constructed to regularize the number of mixture components. Our algorithm gives a risk bound that trades off between prediction accuracy and model sparsity without imposing stringent assumptions on the input/output distribution, and can be easily adapted to the case of non-linear functions.

Beam search is widely used for approximate decoding in structured prediction problems. Models often use a beam at test time but ignore its existence at train time, and therefore do not explicitly learn how to use the beam. We develop an unifying meta-algorithm for learning beam search policies using imitation learning. In our setting, the beam is part of the model and not just an artifact of approximate decoding. Our meta-algorithm captures existing learning algorithms and suggests new ones.